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andreev551 [17]
2 years ago
8

Which number line represtents the solution to |x+4|=2?​

Mathematics
1 answer:
vlada-n [284]2 years ago
7 0

Answer:

Points -2 and -6 on the number line are the two solutions.

Step-by-step explanation:

Use the definition of absolute value as a starting point

|x|=x\,\,\mbox{for}\,\,x\geq 0\\|x|=-x\,\,\mbox{for}\,\,x

To solve the equation, you need to treat the two cases as above:

|x+4|=x+4=2\,\,\,\mbox{for}\,\,x+4\geq 0\implies x\geq -4\\x+4=2\implies x=-2

The solution x=-2 is consistent with the condition x>=-4, so it is the first and valid solution. Now the second case of the absolute value:

|x+4|=-(x+4)=2\,\,\,\mbox{for}\,\,x+4< 0\implies x

Again, the second solution -6 complies with the requirement that x<-4, so it is valid.

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-3+9-27+81-243+729. Using the sigma notation to write the given sum
IgorC [24]

Answer:

546

Step-by-step explanation:

5 0
3 years ago
What are or is function? <br>(Please explain in you your word)​
podryga [215]

Answer:

In mathematics, a function is a binary relation between two sets that associates every element of the first set to exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers.

Step-by-step explanation:

8 0
3 years ago
Can someone help me here<br><br> NONSENSE=REPORT​
lys-0071 [83]

\huge \qquad \sf \: Answer

Here we go ~

1. A circle can be named by their Centre, so here in the diagram it's :

  • Circle A

2. Name 4 radii :

Radii are the line segments that joins the centre and boundary of circle.

They are :

  • FA
  • GA
  • BA
  • CA

3. 2 Major arcs :

considering two points on a circle, and joining them forms a curve ( you can say part of circumference )

When we consider two points two arcs are formed and the arc with more length is known as Major Arc

That is :

  • Major arc ECF
  • Major arc BEC

4. A Semicircle :

Semicircle is special arc which is formed when two arcs formed by the points are equals to one another... it's also half the Perimeter of circle.

that is :

  • Arc CF is a Semicircle

5. 3 minor arcs :

The arc formed by two points having lesser length is known as minor arc.

that is :

  • Arc EF
  • Arc BG
  • Arc FG

6. 3 Central angles :

Central angles are angles formed by arcs on centre of the circle ~

that is :

  • Angle FAB
  • Angle BAC
  • Angle GAB

7. A diameter :

Diameter is a chord that passes through centre of the circle.

  • CF

8. Congruent Angles :

In the given figure, there are two equal/congruent angles that are ~

  • Angle BAG and Angle GAF

9. Adjacent arcs :

The arcs that have one common end point are known as Adjacent arcs ~

that are :

  • Arc FG and Arc GB

4 0
2 years ago
Read 2 more answers
You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
anyanavicka [17]

9514 1404 393

Answer:

  • loan: $157,823
  • repaid: $378,000
  • interest: $220,177

Step-by-step explanation:

For a loan value of 1, the monthly payment on a 30 year loan at 7% is ...

  A = (0.07/12)/(1 -(1 +0.07/12)^(-12·30)) ≈ 0.00665302495

Then the amount repaid after 360 payments is ...

  360A = 2.39508898 . . . times the principal amount

__

a) For a monthly payment of $1050, the principal can be ...

  $1050/0.00665302495 ≈ $157,823

__

b) The amount repaid to the loan company is ...

  $157,823×2.39508898 ≈ $378,000

__

c) The amount that is interest is ...

  $378,000 -157,823 = $220,177

8 0
3 years ago
A local car dealer claims that 25% of all cars in San Francisco are blue. You take a random sample of 600 cars in San Francisco
sammy [17]

Answer:

No, we can't reject the dealer's claim with a significance level of 0.05.

Step-by-step explanation:

We are given that a local car dealer claims that 25% of all cars in San Francisco are blue.

You take a random sample of 600 cars in San Francisco and find that 141 are blue.

<u><em>Let p = proportion of all cars in San Francisco who are blue</em></u>

SO, Null Hypothesis, H_0 : p = 25%   {means that 25% of all cars in San Francisco are blue}

Alternate Hypothesis, H_A : p \neq 25%   {means that % of all cars in San Francisco who are blue is different from 25%}

The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;

                                  T.S.  = \frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }  ~ N(0,1)

where, \hat p = sample proportion of 600 cars in San Francisco who are blue =   \frac{141}{600} = 0.235

            n = sample of cars = 600

So, <u><em>test statistics</em></u>  =  \frac{0.235-0.25}{{\sqrt{\frac{0.235(1-0.235)}{600} } } } }

                               =  -0.866

<em>Now at 0.05 significance level, the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>

Therefore, we conclude that 25% of all cars in San Francisco are blue which means the dealer's claim was correct.

4 0
3 years ago
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